Linear combinations of normal random variables: weed trimmer production
The production of a brand of weed trimmer involves three stages, Stage 1, Stage 2 and Stage 3, which take hours, hours and hours, respectively. Here , and are independent random variables, which may be assumed to be normally distributed. Assume that Stage 2 starts immediately after Stage 1 ends and that Stage 3 starts immediately after Stage 2 ends.
Find the mean and the variance of the total time to produce one weed trimmer.
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Find the variance of the total cost to produce one weed trimmer.
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If a single weed trimmer is produced, find the probability that the time spent at Stage 2 will be less than the time spent at Stage 1.
Give your answer correct to two decimal places.
Use , where is the standard normal variable with mean 0 and standard deviation 1.
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